A novel method for fractal-fractional differential equations

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dc.contributor.authorAttia, Nourhane
dc.contributor.authorAkgul, Ali
dc.contributor.authorSeba, Djamila
dc.contributor.authorNour, Abdelkader
dc.contributor.authorAsad, Jihad
dc.date.accessioned2024-12-24T19:25:12Z
dc.date.available2024-12-24T19:25:12Z
dc.date.issued2022
dc.departmentSiirt Üniversitesi
dc.description.abstractWe consider the reproducing kernel Hilbert space method to construct numerical solutions for some basic fractional ordinary differential equations (FODEs) under fractal fractional derivative with the generalized Mittag-Leffler (M-L) kernel. Deriving the analytic and numerical solutions of this new class of differential equations are modern trends. To apply this method, we use reproducing kernel theory and two important Hilbert spaces. We provide three problems to illustrate our main results including the profiles of different representative approximate solutions. The computational results are compared with the exact solutions. The results obtained clearly show the effect of the fractal fractional derivative with the M-L kernel in the obtained outcomes. Meanwhile, the compatibility between the approximate and exact solutions confirms the applicability and superior performance of the method. (c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/
dc.description.sponsorshipPTUK
dc.description.sponsorshipJ. Asad would like to thank PTUK for their financial support.
dc.identifier.doi10.1016/j.aej.2022.02.004
dc.identifier.endpage9748
dc.identifier.issn1110-0168
dc.identifier.issn2090-2670
dc.identifier.issue12
dc.identifier.scopus2-s2.0-85125747592
dc.identifier.scopusqualityQ1
dc.identifier.startpage9733
dc.identifier.urihttps://doi.org/10.1016/j.aej.2022.02.004
dc.identifier.urihttps://hdl.handle.net/20.500.12604/6312
dc.identifier.volume61
dc.identifier.wosWOS:000806179500005
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherElsevier
dc.relation.ispartofAlexandria Engineering Journal
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241222
dc.subjectReproducing kernel Hilbert space method
dc.subjectGram-Schmidt orthogonal-ization process
dc.subjectFractal-fractional derivative
dc.subjectMittag-Leffler kernel
dc.titleA novel method for fractal-fractional differential equations
dc.typeArticle

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